It is a combination of electric repulsion and the Pauli exclusion principle.
Electric repulsion means that when atoms get too close, the electrons on the outside of the atoms repel each other because they are both negatively charged.
Pauli exclusion is a quantum effect that prevents particles from overlapping too much in space. It is different from electric repulsion, but the consequence is similar, providing an extra repulsive effect between particles of the same type (i.e. electrons don’t want to sit too much on top of other electrons).
These work together to make it so that, if atoms get too closer together, they push on each other and try to spread back out. That keeps the Earth large because, though gravity is pulling it inward, all that molten rock can’t become too dense, because the atoms are pushing on each other too much. It also keeps us from falling through the ground, because the atoms in our feet/shoes experience these repulsive effects when getting too close to the atoms in the ground.
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